The mantissa distribution of the primorial numbers

Bruno Massé, and Dominique Schneider. "The mantissa distribution of the primorial numbers." Acta Arithmetica 163.1 (2014): 45-58. <http://eudml.org/doc/279327>.

@article{BrunoMassé2014,
abstract = {We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.},
author = {Bruno Massé, Dominique Schneider},
journal = {Acta Arithmetica},
keywords = {Benford's law; uniform distribution; weighted distribution; prime number},
language = {eng},
number = {1},
pages = {45-58},
title = {The mantissa distribution of the primorial numbers},
url = {http://eudml.org/doc/279327},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Bruno Massé
AU - Dominique Schneider
TI - The mantissa distribution of the primorial numbers
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 1
SP - 45
EP - 58
AB - We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.
LA - eng
KW - Benford's law; uniform distribution; weighted distribution; prime number
UR - http://eudml.org/doc/279327
ER -